MR. G. A. SCHOTT ON THE REFLECTION AND REFRACTION OF LIGHT. 855 
large part of r to be — sin is negative, so that for parallel-polarized 
light at normal incidence the vibration in the reflected light is opposite to that in the 
incident at the reflecting surface, so that there is a retardation of phase = tt. 
Similarly, the equations (VI'.) give for the important part of r for perpendicularly- 
polarized light — ^— .? . which is negative at normal incidence, but positive for 
^ tan + % y ) 
incidences greater than the polarizing angle. 
We shall suppose II 11, R X to be taken equal to the absolute values of the above 
ratios. Then p 11 will lie between tt and 2??, or between tt and 0, according as 
tan (p II) is + or —, and will differ from tt by an amount of the order S. The same 
will apply to p X, whose difference from tt, however, does not remain of order S, but 
which increases through 37r/2 to 27r, or decreases through \tt to 0, according to the 
sign of tan (p X). 
The difference p X — p 11 —the retardation of phase of the perpendicularly- over the 
parallel-polarized light—is positive or negative according as tan (p X) is positive or 
negative, and increases numerically from 0 at normal incidence through X at the 
polarizing angle to X tt at grazing incidence. And the reflection is said by Jamin to 
be positive or negative as the case may be. 
If a ray of elliptically-polarized light be reflected normally from a surface, then the 
difference of phase of the components, and the position of the axes of the vibrational 
ellipse, as well as the direction of its description, are all unchanged in space, but with 
reference to the direction of propagation, and, therefore, also to an observer viewing 
both rays, the position of the axes has changed into one symmetrical to the former 
one, with respect to the plane of incidence, and the ray from being right-handed has 
become left-handed, or vice versd. Thus, there is an apparent change of phase of tt, 
which is called by Jamin “tt de retournement,” and causes him to give the measured 
difference of phase as lying between tt and 27r, instead of between 0 and tt. 
We must also consider the effect of a finite, though large, velocity for the pressural 
wave in the Elastic Solid Theory. We have made no supposition as to the values of 
the m’s, the ratios of the pressural-wave velocity to that of light in the different 
media, except that these ratios are large. The ratio may have any value, so 
that the refractive index for the pressural-wave between the two media may also have 
any value. The effect of the pressural-wave is to add to 
/^r 
/^o' 
a quantity 
^ ^ -r ^.—, for moderately-large values of such as are used in most 
of the experiments; in (R X)®, also, there is an additional term, which at no angle of 
incidence is of magnitude more than comparable with 1/r//^. 
Now is large, perhaps 100, as above, § 3, p. 834. The term in (RX)^ may always 
be neglected; and at all but very small angles of incidence M be put equal to 
